Solve for $y$, $ \dfrac{10}{y - 3} = -\dfrac{9}{5y - 15} + \dfrac{2y - 4}{5y - 15} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $y - 3$ $5y - 15$ and $5y - 15$ The common denominator is $5y - 15$ To get $5y - 15$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{10}{y - 3} \times \dfrac{5}{5} = \dfrac{50}{5y - 15} $ The denominator of the second term is already $5y - 15$ , so we don't need to change it. The denominator of the third term is already $5y - 15$ , so we don't need to change it. This give us: $ \dfrac{50}{5y - 15} = -\dfrac{9}{5y - 15} + \dfrac{2y - 4}{5y - 15} $ If we multiply both sides of the equation by $5y - 15$ , we get: $ 50 = -9 + 2y - 4$ $ 50 = 2y - 13$ $ 63 = 2y $ $ y = \dfrac{63}{2}$